Estimation Algorithm
Adaptive estimation algorithms calculate time varying parameters of dynamic systems by fitting mathematical models to streaming sensor output. The directional forgetting recursive least squares method implements this estimation by scaling down the information matrix only in the direction of the incoming excitation. This selective attenuation avoids the numerical explosion that occurs when a global forgetting factor is applied to inactive states.
Information Weighting
Standard recursive algorithms discard historical data uniformly across all states, causing the covariance matrix to grow unboundedly when some parameters are not excited. Selective forgetting counters this by analyzing the projection of the data vector on the parameter space. The algorithm calculates an excitation threshold and only applies the forgetting factor to the active subspace, while holding the information in the quiet directions constant.
Signal Tracking
Tracking dynamics are tested by introducing sudden step changes in specific system parameters during periods of uneven sensor activity. This approach provides rapid adaptation to genuine changes without introducing fictitious parameter drift in unexcited directions. Engineering teams evaluate the convergence speed using controlled simulated datasets.
Stability Constraint
Mathematical limits restrict the application of directional forgetting in systems with highly correlated noise or persistent structural feedback. If the excitation falls below the measurement noise floor, the algorithm can still suffer from wind up unless a lower bound is enforced on the information matrix eigenvalues. The calibration engineer configures these bounds to maintain numerical stability in the processor.
